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‘Big Questions’ : Valuation How do we decide on whether … How do we decide on whether … –… to undertake a new (physical) investment project ? –... to buy a potential ’takeover target’ ? –… to buy stocks, bonds and other financial instruments (including foreign assets) ? To determine the above we need to calculate the ‘correct’ or ‘fair’ value V of the future cash flows from these ‘assets’. To determine the above we need to calculate the ‘correct’ or ‘fair’ value V of the future cash flows from these ‘assets’. If V > P (price of stock) or V > capital cost of project then purchase ‘asset’.

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‘Big Questions’ : Risk How do we take account of the ‘riskiness of the future cash flows when determining the fair value of these assets (e.g. stocks, investment project) ? How do we take account of the ‘riskiness of the future cash flows when determining the fair value of these assets (e.g. stocks, investment project) ? A. : Use Discounted Present Value Model (DPV) where the discount rate should reflect the riskiness of the future cash flows from the asset  CAPM A. : Use Discounted Present Value Model (DPV) where the discount rate should reflect the riskiness of the future cash flows from the asset  CAPM

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‘Big Questions’ Portfolio Theory : Portfolio Theory : –Can we combine several assets in order to reduce risk while still maintaining some ‘return’ ?  Portfolio theory, international diversification Hedging : Hedging : –Can we combine several assets in order to reduce risk to (near) zero ?  hedging with derivatives Speculation : Speculation : –Can ‘stock pickers’ ‘beat the market’ return (i.e. index tracker on S&P500), over a run of bets, after correcting for risk and transaction costs ?

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Example : PV, FV, NPV, IRR Question : How much money must I invest in a comparable investment of similar risk to duplicate exactly the cash flows of this investments ? Case : You can invest in a company and your investment (today) of £ 100,000 will be worth (with certainty) £ 160,000 one year from today. Similar investments earn 20% p.a. !

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Annuity Future payments are constant in each year : FV i = $C Future payments are constant in each year : FV i = $C First payment is at the end of the first year First payment is at the end of the first year Ordinary annuity Ordinary annuity DPV = C  1/(1+r) i Formula for sum of geometric progression Formula for sum of geometric progression DPV = CA n,r where A n,r = (1/r) [1- 1/(1+r) n ] DPV = C/rfor n  ∞

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Investment Decision Invest in the project if : Invest in the project if : DPV > KCor NPV > 0 IRR > r if DPV = KC or if IRR is just equal the opportunity cost of the fund, then investment project will just pay back the principal and interest on loan. If DPV = KC  IRR = r If DPV = KC  IRR = r

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Summary of NPV and IRR NPV and IRR give identical decisions for independent projects with ‘normal cash flows’ NPV and IRR give identical decisions for independent projects with ‘normal cash flows’ For cash flows which change sign more than once, the IRR gives multiple solutions and cannot be used  use NPV For cash flows which change sign more than once, the IRR gives multiple solutions and cannot be used  use NPV For mutually exclusive projects use the NPV criterion For mutually exclusive projects use the NPV criterion